//1314.矩阵区域和
class Solution {
    public int[][] matrixBlockSum(int[][] mat, int k) {
        int m = mat.length, n = mat[0].length;
        // 1. 预处理前缀和矩阵
        int[][] dp = new int[m + 1][n + 1];
        for (int i = 1; i <= m; i++)
            for (int j = 1; j <= n; j++)
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1] - dp[i - 1][j - 1] +
                        mat[i - 1][j - 1];

        // 2. 使⽤
        int[][] ret = new int[m][n];
        for (int i = 0; i < m; i++)
            for (int j = 0; j < n; j++) {
                int x1 = Math.max(0, i - k) + 1, y1 = Math.max(0, j - k) + 1;
                int x2 = Math.min(m - 1, i + k) + 1, y2 = Math.min(n - 1, j +
                        k) + 1;
                ret[i][j] = dp[x2][y2] - dp[x1 - 1][y2] - dp[x2][y1 - 1] +
                        dp[x1 - 1][y1 - 1];
            }
        return ret;
    }
}
